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Systems of Two Linear Equations in Two Variables

SAT Math· difficulty 3/5

What point is the intersection of x−3y=1x - 3y = 1 and 2x+y=92x + y = 9?

  • A

    (4,1)(4, 1)

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  • B

    (2,13)(2, \frac{1}{3})

  • C

    (2,13(2, \frac{1}{3})$

  • D

    (3,3)(3, 3)

Explanation

From eq1: x=1+3yx = 1 + 3y. Sub: 2(1+3y)+y=92(1+3y) + y = 9 → 7y=77y = 7 → y=1y = 1, x=4x = 4.

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